Heterogeneous face recognition (HFR) refers to matching face imagery across different domains. It has received much interest from the research community as a result of its profound implications in law enforcement. A wide variety of new invariant features, cross-modality matching models and heterogeneous datasets are being established in recent years. This survey provides a comprehensive review of established techniques and recent developments in HFR. Moreover, we offer a detailed account of datasets and benchmarks commonly used for evaluation. We finish by assessing the state of the field and discussing promising directions for future research.